Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class A {
	
	public static void main(String[] args) {
		Scanner theIn=new Scanner(System.in);
		int n=theIn.nextInt();
		int t=(int) Math.sqrt((double) n);
		int left;
		boolean result=false;
		for (int i=1; i<=t; i++) {
			left=(n-i*(i+1)/2)*2;
			int m=(int) Math.floor(Math.sqrt(left));
			if (m==0) continue;
			if (m*(m+1)==left) {
				result=true;
				break;
			}
		}
		if (result) System.out.println("YES");
		else System.out.println("NO");
	}
}